LMFDB - Embedded newform 1050.3.c.c.449.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.31
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.32

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(2.92855 - 0.650833i) q^{3} +2.00000 q^{4} +(4.14160 - 0.920417i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(8.15283 - 3.81200i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(2.92855 - 0.650833i) q^{3} +2.00000 q^{4} +(4.14160 - 0.920417i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(8.15283 - 3.81200i) q^{9} +7.97556i q^{11} +(5.85710 - 1.30167i) q^{12} +5.79363i q^{13} -3.74166i q^{14} +4.00000 q^{16} -9.35782 q^{17} +(11.5298 - 5.39098i) q^{18} +22.7979 q^{19} +(-1.72194 - 7.74822i) q^{21} +11.2792i q^{22} +34.9882 q^{23} +(8.28320 - 1.84083i) q^{24} +8.19343i q^{26} +(21.3950 - 16.4698i) q^{27} -5.29150i q^{28} -15.5858i q^{29} +25.5869 q^{31} +5.65685 q^{32} +(5.19076 + 23.3569i) q^{33} -13.2340 q^{34} +(16.3057 - 7.62399i) q^{36} +38.4908i q^{37} +32.2412 q^{38} +(3.77068 + 16.9669i) q^{39} -35.1062i q^{41} +(-2.43519 - 10.9576i) q^{42} -59.0951i q^{43} +15.9511i q^{44} +49.4808 q^{46} +1.03517 q^{47} +(11.7142 - 2.60333i) q^{48} -7.00000 q^{49} +(-27.4049 + 6.09038i) q^{51} +11.5873i q^{52} -41.5179 q^{53} +(30.2571 - 23.2918i) q^{54} -7.48331i q^{56} +(66.7650 - 14.8377i) q^{57} -22.0417i q^{58} -55.1602i q^{59} -94.7726 q^{61} +36.1853 q^{62} +(-10.0856 - 21.5704i) q^{63} +8.00000 q^{64} +(7.34084 + 33.0316i) q^{66} +77.1064i q^{67} -18.7156 q^{68} +(102.465 - 22.7715i) q^{69} +18.0046i q^{71} +(23.0597 - 10.7820i) q^{72} -33.2022i q^{73} +54.4342i q^{74} +45.5959 q^{76} +21.1014 q^{77} +(5.33255 + 23.9949i) q^{78} +54.9427 q^{79} +(51.9374 - 62.1571i) q^{81} -49.6477i q^{82} -78.6593 q^{83} +(-3.44388 - 15.4964i) q^{84} -83.5731i q^{86} +(-10.1438 - 45.6439i) q^{87} +22.5583i q^{88} +120.028i q^{89} +15.3285 q^{91} +69.9764 q^{92} +(74.9326 - 16.6528i) q^{93} +1.46395 q^{94} +(16.5664 - 3.68167i) q^{96} +24.5127i q^{97} -9.89949 q^{98} +(30.4028 + 65.0234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	2.92855	−	0.650833i	0.976184	−	0.216944i
$3$	2.92855	−	0.650833i	0.976184	−	0.216944i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	4.14160	−	0.920417i	0.690266	−	0.153403i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	2.82843			0.353553
$9$	8.15283	−	3.81200i	0.905870	−	0.423555i
$10$		0			0
$11$			7.97556i			0.725051i	0.931974	+	0.362526i	$0.118085\pi$
$11$			7.97556i			0.725051i	−0.931974	+	0.362526i	$0.881915\pi$
$12$	5.85710	−	1.30167i	0.488092	−	0.108472i
$13$			5.79363i			0.445664i	0.974857	+	0.222832i	$0.0715301\pi$
$13$			5.79363i			0.445664i	−0.974857	+	0.222832i	$0.928470\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−9.35782			−0.550460			−0.275230	−	0.961378i	$-0.588754\pi$
$17$	−9.35782			−0.550460			−0.275230	+	0.961378i	$0.588754\pi$
$18$	11.5298	−	5.39098i	0.640547	−	0.299499i
$19$	22.7979			1.19989			0.599946	−	0.800041i	$-0.295189\pi$
$19$	22.7979			1.19989			0.599946	+	0.800041i	$0.295189\pi$
$20$		0			0
$21$	−1.72194	−	7.74822i	−0.0819972	−	0.368963i
$22$			11.2792i			0.512689i
$23$	34.9882			1.52123			0.760613	−	0.649205i	$-0.224898\pi$
$23$	34.9882			1.52123			0.760613	+	0.649205i	$0.224898\pi$
$24$	8.28320	−	1.84083i	0.345133	−	0.0767014i
$25$		0			0
$26$			8.19343i			0.315132i
$27$	21.3950	−	16.4698i	0.792408	−	0.609991i
$28$		−	5.29150i		−	0.188982i
$29$		−	15.5858i		−	0.537442i	−0.963218	−	0.268721i	$-0.913399\pi$
$29$		−	15.5858i		−	0.537442i	0.963218	−	0.268721i	$-0.0866010\pi$
$30$		0			0
$31$	25.5869			0.825384			0.412692	−	0.910871i	$-0.364589\pi$
$31$	25.5869			0.825384			0.412692	+	0.910871i	$0.364589\pi$
$32$	5.65685			0.176777
$33$	5.19076	+	23.3569i	0.157296	+	0.707783i
$34$	−13.2340			−0.389234
$35$		0			0
$36$	16.3057	−	7.62399i	0.452935	−	0.211778i
$37$			38.4908i			1.04029i	0.854078	+	0.520145i	$0.174122\pi$
$37$			38.4908i			1.04029i	−0.854078	+	0.520145i	$0.825878\pi$
$38$	32.2412			0.848451
$39$	3.77068	+	16.9669i	0.0966842	+	0.435050i
$40$		0			0
$41$		−	35.1062i		−	0.856249i	−0.903720	−	0.428125i	$-0.859174\pi$
$41$		−	35.1062i		−	0.856249i	0.903720	−	0.428125i	$-0.140826\pi$
$42$	−2.43519	−	10.9576i	−0.0579808	−	0.260896i
$43$		−	59.0951i		−	1.37431i	−0.726513	−	0.687153i	$-0.758860\pi$
$43$		−	59.0951i		−	1.37431i	0.726513	−	0.687153i	$-0.241140\pi$
$44$			15.9511i			0.362526i
$45$		0			0
$46$	49.4808			1.07567
$47$	1.03517			0.0220249			0.0110124	−	0.999939i	$-0.496495\pi$
$47$	1.03517			0.0220249			0.0110124	+	0.999939i	$0.496495\pi$
$48$	11.7142	−	2.60333i	0.244046	−	0.0542361i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−27.4049	+	6.09038i	−0.537351	+	0.119419i
$52$			11.5873i			0.222832i
$53$	−41.5179			−0.783357			−0.391679	−	0.920102i	$-0.628105\pi$
$53$	−41.5179			−0.783357			−0.391679	+	0.920102i	$0.628105\pi$
$54$	30.2571	−	23.2918i	0.560317	−	0.431329i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	66.7650	−	14.8377i	1.17131	−	0.260310i
$58$		−	22.0417i		−	0.380029i
$59$		−	55.1602i		−	0.934919i	−0.884014	−	0.467460i	$-0.845169\pi$
$59$		−	55.1602i		−	0.934919i	0.884014	−	0.467460i	$-0.154831\pi$
$60$		0			0
$61$	−94.7726			−1.55365			−0.776824	−	0.629717i	$-0.783171\pi$
$61$	−94.7726			−1.55365			−0.776824	+	0.629717i	$0.783171\pi$
$62$	36.1853			0.583635
$63$	−10.0856	−	21.5704i	−0.160089	−	0.342387i
$64$	8.00000			0.125000
$65$		0			0
$66$	7.34084	+	33.0316i	0.111225	+	0.500478i
$67$			77.1064i			1.15084i	0.817857	+	0.575421i	$0.195162\pi$
$67$			77.1064i			1.15084i	−0.817857	+	0.575421i	$0.804838\pi$
$68$	−18.7156			−0.275230
$69$	102.465	−	22.7715i	1.48500	−	0.330021i
$70$		0			0
$71$			18.0046i			0.253586i	0.991929	+	0.126793i	$0.0404684\pi$
$71$			18.0046i			0.253586i	−0.991929	+	0.126793i	$0.959532\pi$
$72$	23.0597	−	10.7820i	0.320274	−	0.149749i
$73$		−	33.2022i		−	0.454825i	−0.973799	−	0.227412i	$-0.926973\pi$
$73$		−	33.2022i		−	0.454825i	0.973799	−	0.227412i	$-0.0730266\pi$
$74$			54.4342i			0.735597i
$75$		0			0
$76$	45.5959			0.599946
$77$	21.1014			0.274044
$78$	5.33255	+	23.9949i	0.0683660	+	0.307627i
$79$	54.9427			0.695478			0.347739	−	0.937591i	$-0.386950\pi$
$79$	54.9427			0.695478			0.347739	+	0.937591i	$0.386950\pi$
$80$		0			0
$81$	51.9374	−	62.1571i	0.641202	−	0.767372i
$82$		−	49.6477i		−	0.605460i
$83$	−78.6593			−0.947703			−0.473851	−	0.880605i	$-0.657137\pi$
$83$	−78.6593			−0.947703			−0.473851	+	0.880605i	$0.657137\pi$
$84$	−3.44388	−	15.4964i	−0.0409986	−	0.184481i
$85$		0			0
$86$		−	83.5731i		−	0.971781i
$87$	−10.1438	−	45.6439i	−0.116595	−	0.524643i
$88$			22.5583i			0.256344i
$89$			120.028i			1.34863i	0.738442	+	0.674317i	$0.235562\pi$
$89$			120.028i			1.34863i	−0.738442	+	0.674317i	$0.764438\pi$
$90$		0			0
$91$	15.3285			0.168445
$92$	69.9764			0.760613
$93$	74.9326	−	16.6528i	0.805727	−	0.179062i
$94$	1.46395			0.0155739
$95$		0			0
$96$	16.5664	−	3.68167i	0.172567	−	0.0383507i
$97$			24.5127i			0.252708i	0.991985	+	0.126354i	$0.0403276\pi$
$97$			24.5127i			0.252708i	−0.991985	+	0.126354i	$0.959672\pi$
$98$	−9.89949			−0.101015
$99$	30.4028	+	65.0234i	0.307099	+	0.656802i
$100$		0			0
$101$			158.695i			1.57124i	0.618709	+	0.785620i	$0.287656\pi$
$101$			158.695i			1.57124i	−0.618709	+	0.785620i	$0.712344\pi$
$102$	−38.7563	+	8.61310i	−0.379964	+	0.0844421i
$103$		−	177.505i		−	1.72335i	−0.507461	−	0.861674i	$-0.669416\pi$
$103$		−	177.505i		−	1.72335i	0.507461	−	0.861674i	$-0.330584\pi$
$104$			16.3869i			0.157566i
$105$		0			0
$106$	−58.7152			−0.553917
$107$	−210.992			−1.97189			−0.985946	−	0.167064i	$-0.946571\pi$
$107$	−210.992			−1.97189			−0.985946	+	0.167064i	$0.946571\pi$
$108$	42.7900	−	32.9395i	0.396204	−	0.304996i
$109$	98.5237			0.903887			0.451943	−	0.892047i	$-0.350731\pi$
$109$	98.5237			0.903887			0.451943	+	0.892047i	$0.350731\pi$
$110$		0			0
$111$	25.0511	+	112.722i	0.225685	+	1.01552i
$112$		−	10.5830i		−	0.0944911i
$113$	−102.830			−0.910000			−0.455000	−	0.890492i	$-0.650361\pi$
$113$	−102.830			−0.910000			−0.455000	+	0.890492i	$0.650361\pi$
$114$	94.4199	−	20.9836i	0.828245	−	0.184067i
$115$		0			0
$116$		−	31.1717i		−	0.268721i
$117$	22.0853	+	47.2345i	0.188763	+	0.403713i
$118$		−	78.0084i		−	0.661088i
$119$			24.7585i			0.208054i
$120$		0			0
$121$	57.3904			0.474301
$122$	−134.029			−1.09860
$123$	−22.8483	−	102.810i	−0.185758	−	0.835857i
$124$	51.1738			0.412692
$125$		0			0
$126$	−14.2632	−	30.5051i	−0.113200	−	0.242104i
$127$			157.688i			1.24164i	0.783954	+	0.620819i	$0.213200\pi$
$127$			157.688i			1.24164i	−0.783954	+	0.620819i	$0.786800\pi$
$128$	11.3137			0.0883883
$129$	−38.4611	−	173.063i	−0.298148	−	1.34158i
$130$		0			0
$131$			250.120i			1.90932i	0.297705	+	0.954658i	$0.403779\pi$
$131$			250.120i			1.90932i	−0.297705	+	0.954658i	$0.596221\pi$
$132$	10.3815	+	46.7137i	0.0786479	+	0.353892i
$133$		−	60.3177i		−	0.453516i
$134$			109.045i			0.813768i
$135$		0			0
$136$	−26.4679			−0.194617
$137$	−191.896			−1.40070			−0.700350	−	0.713800i	$-0.746973\pi$
$137$	−191.896			−1.40070			−0.700350	+	0.713800i	$0.746973\pi$
$138$	144.907	−	32.2037i	1.05005	−	0.233360i
$139$	−21.4645			−0.154421			−0.0772103	−	0.997015i	$-0.524601\pi$
$139$	−21.4645			−0.154421			−0.0772103	+	0.997015i	$0.524601\pi$
$140$		0			0
$141$	3.03155	−	0.673722i	0.0215003	−	0.00477817i
$142$			25.4624i			0.179313i
$143$	−46.2074			−0.323129
$144$	32.6113	−	15.2480i	0.226468	−	0.105889i
$145$		0			0
$146$		−	46.9550i		−	0.321610i
$147$	−20.4999	+	4.55583i	−0.139455	+	0.0309920i
$148$			76.9815i			0.520145i
$149$		−	66.8671i		−	0.448772i	−0.974500	−	0.224386i	$-0.927962\pi$
$149$		−	66.8671i		−	0.448772i	0.974500	−	0.224386i	$-0.0720377\pi$
$150$		0			0
$151$	−64.4712			−0.426962			−0.213481	−	0.976947i	$-0.568480\pi$
$151$	−64.4712			−0.426962			−0.213481	+	0.976947i	$0.568480\pi$
$152$	64.4823			0.424226
$153$	−76.2928	+	35.6720i	−0.498646	+	0.233150i
$154$	29.8418			0.193778
$155$		0			0
$156$	7.54137	+	33.9339i	0.0483421	+	0.217525i
$157$		−	207.257i		−	1.32011i	−0.751217	−	0.660056i	$-0.770533\pi$
$157$		−	207.257i		−	1.32011i	0.751217	−	0.660056i	$-0.229467\pi$
$158$	77.7008			0.491777
$159$	−121.587	+	27.0212i	−0.764701	+	0.169945i
$160$		0			0
$161$		−	92.5701i		−	0.574970i
$162$	73.4505	−	87.9035i	0.453398	−	0.542614i
$163$		−	236.067i		−	1.44826i	−0.689662	−	0.724132i	$-0.742241\pi$
$163$		−	236.067i		−	1.44826i	0.689662	−	0.724132i	$-0.257759\pi$
$164$		−	70.2124i		−	0.428125i
$165$		0			0
$166$	−111.241			−0.670127
$167$	−109.647			−0.656568			−0.328284	−	0.944579i	$-0.606470\pi$
$167$	−109.647			−0.656568			−0.328284	+	0.944579i	$0.606470\pi$
$168$	−4.87039	−	21.9153i	−0.0289904	−	0.130448i
$169$	135.434			0.801384
$170$		0			0
$171$	185.868	−	86.9057i	1.08695	−	0.508220i
$172$		−	118.190i		−	0.687153i
$173$	46.7105			0.270003			0.135001	−	0.990845i	$-0.456896\pi$
$173$	46.7105			0.270003			0.135001	+	0.990845i	$0.456896\pi$
$174$	−14.3455	−	64.5502i	−0.0824452	−	0.370978i
$175$		0			0
$176$			31.9023i			0.181263i
$177$	−35.9001	−	161.540i	−0.202825	−	0.912653i
$178$			169.746i			0.953629i
$179$			293.828i			1.64150i	0.571289	+	0.820749i	$0.306444\pi$
$179$			293.828i			1.64150i	−0.571289	+	0.820749i	$0.693556\pi$
$180$		0			0
$181$	−129.626			−0.716168			−0.358084	−	0.933689i	$-0.616570\pi$
$181$	−129.626			−0.716168			−0.358084	+	0.933689i	$0.616570\pi$
$182$	21.6778			0.119109
$183$	−277.546	+	61.6811i	−1.51665	+	0.337055i
$184$	98.9616			0.537835
$185$		0			0
$186$	105.971	−	23.5506i	0.569735	−	0.126616i
$187$		−	74.6339i		−	0.399112i
$188$	2.07034			0.0110124
$189$	−43.5749	−	56.6059i	−0.230555	−	0.299502i
$190$		0			0
$191$			7.24400i			0.0379267i	0.999820	+	0.0189633i	$0.00603658\pi$
$191$			7.24400i			0.0379267i	−0.999820	+	0.0189633i	$0.993963\pi$
$192$	23.4284	−	5.20666i	0.122023	−	0.0271180i
$193$			313.671i			1.62524i	0.582793	+	0.812620i	$0.301960\pi$
$193$			313.671i			1.62524i	−0.582793	+	0.812620i	$0.698040\pi$
$194$			34.6662i			0.178692i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−94.5137			−0.479765			−0.239882	−	0.970802i	$-0.577109\pi$
$197$	−94.5137			−0.479765			−0.239882	+	0.970802i	$0.577109\pi$
$198$	42.9961	+	91.9570i	0.217152	+	0.464429i
$199$	185.816			0.933747			0.466874	−	0.884324i	$-0.345380\pi$
$199$	185.816			0.933747			0.466874	+	0.884324i	$0.345380\pi$
$200$		0			0
$201$	50.1834	+	225.810i	0.249669	+	1.12343i
$202$			224.429i			1.11104i
$203$	−41.2362			−0.203134
$204$	−54.8098	+	12.1808i	−0.268675	+	0.0597096i
$205$		0			0
$206$		−	251.030i		−	1.21859i
$207$	285.253	−	133.375i	1.37803	−	0.644323i
$208$			23.1745i			0.111416i
$209$			181.826i			0.869983i
$210$		0			0
$211$	375.709			1.78061			0.890306	−	0.455363i	$-0.150491\pi$
$211$	375.709			1.78061			0.890306	+	0.455363i	$0.150491\pi$
$212$	−83.0359			−0.391679
$213$	11.7180	+	52.7275i	0.0550141	+	0.247547i
$214$	−298.388			−1.39434
$215$		0			0
$216$	60.5143	−	46.5835i	0.280159	−	0.215664i
$217$		−	67.6966i		−	0.311966i
$218$	139.334			0.639145
$219$	−21.6091	−	97.2344i	−0.0986717	−	0.443993i
$220$		0			0
$221$		−	54.2158i		−	0.245320i
$222$	35.4275	+	159.413i	0.159584	+	0.718078i
$223$			19.6107i			0.0879404i	0.999033	+	0.0439702i	$0.0140007\pi$
$223$			19.6107i			0.0879404i	−0.999033	+	0.0439702i	$0.985999\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−145.424			−0.643467
$227$	−250.934			−1.10543			−0.552717	−	0.833369i	$-0.686409\pi$
$227$	−250.934			−1.10543			−0.552717	+	0.833369i	$0.686409\pi$
$228$	133.530	−	29.6753i	0.585657	−	0.130155i
$229$	−296.680			−1.29555			−0.647773	−	0.761833i	$-0.724299\pi$
$229$	−296.680			−1.29555			−0.647773	+	0.761833i	$0.724299\pi$
$230$		0			0
$231$	61.7964	−	13.7335i	0.267517	−	0.0594522i
$232$		−	44.0834i		−	0.190015i
$233$	−157.483			−0.675891			−0.337946	−	0.941166i	$-0.609732\pi$
$233$	−157.483			−0.675891			−0.337946	+	0.941166i	$0.609732\pi$
$234$	31.2333	+	66.7996i	0.133476	+	0.285469i
$235$		0			0
$236$		−	110.320i		−	0.467460i
$237$	160.903	−	35.7586i	0.678914	−	0.150880i
$238$			35.0138i			0.147117i
$239$			78.7765i			0.329609i	0.986326	+	0.164804i	$0.0526993\pi$
$239$			78.7765i			0.329609i	−0.986326	+	0.164804i	$0.947301\pi$
$240$		0			0
$241$	−148.348			−0.615553			−0.307777	−	0.951459i	$-0.599585\pi$
$241$	−148.348			−0.615553			−0.307777	+	0.951459i	$0.599585\pi$
$242$	81.1623			0.335381
$243$	111.647	−	215.833i	0.459454	−	0.888201i
$244$	−189.545			−0.776824
$245$		0			0
$246$	−32.3124	−	145.396i	−0.131351	−	0.591040i
$247$			132.083i			0.534748i
$248$	72.3707			0.291817
$249$	−230.358	+	51.1941i	−0.925132	+	0.205599i
$250$		0			0
$251$		−	223.217i		−	0.889310i	−0.895702	−	0.444655i	$-0.853326\pi$
$251$		−	223.217i		−	0.889310i	0.895702	−	0.444655i	$-0.146674\pi$
$252$	−20.1712	−	43.1407i	−0.0800444	−	0.171193i
$253$			279.051i			1.10297i
$254$			223.004i			0.877970i
$255$		0			0
$256$	16.0000			0.0625000
$257$	359.930			1.40051			0.700254	−	0.713894i	$-0.253070\pi$
$257$	359.930			1.40051			0.700254	+	0.713894i	$0.253070\pi$
$258$	−54.3922	−	244.748i	−0.210822	−	0.948637i
$259$	101.837			0.393193
$260$		0			0
$261$	−59.4131	−	127.069i	−0.227637	−	0.486853i
$262$			353.724i			1.35009i
$263$	228.402			0.868447			0.434224	−	0.900805i	$-0.357023\pi$
$263$	228.402			0.868447			0.434224	+	0.900805i	$0.357023\pi$
$264$	14.6817	+	66.0632i	0.0556124	+	0.250239i
$265$		0			0
$266$		−	85.3021i		−	0.320685i
$267$	78.1185	+	351.510i	0.292579	+	1.31652i
$268$			154.213i			0.575421i
$269$		−	283.528i		−	1.05401i	−0.849863	−	0.527003i	$-0.823316\pi$
$269$		−	283.528i		−	1.05401i	0.849863	−	0.527003i	$-0.176684\pi$
$270$		0			0
$271$	−290.789			−1.07302			−0.536512	−	0.843893i	$-0.680258\pi$
$271$	−290.789			−1.07302			−0.536512	+	0.843893i	$0.680258\pi$
$272$	−37.4313			−0.137615
$273$	44.8903	−	9.97629i	0.164433	−	0.0365432i
$274$	−271.382			−0.990444
$275$		0			0
$276$	204.930	−	45.5430i	0.742498	−	0.165011i
$277$		−	267.470i		−	0.965596i	−0.875732	−	0.482798i	$-0.839621\pi$
$277$		−	267.470i		−	0.965596i	0.875732	−	0.482798i	$-0.160379\pi$
$278$	−30.3553			−0.109192
$279$	208.606	−	97.5372i	0.747691	−	0.349596i
$280$		0			0
$281$			212.689i			0.756900i	0.925622	+	0.378450i	$0.123543\pi$
$281$			212.689i			0.756900i	−0.925622	+	0.378450i	$0.876457\pi$
$282$	4.28725	−	0.952787i	0.0152030	−	0.00337868i
$283$			249.746i			0.882496i	0.897385	+	0.441248i	$0.145464\pi$
$283$			249.746i			0.882496i	−0.897385	+	0.441248i	$0.854536\pi$
$284$			36.0092i			0.126793i
$285$		0			0
$286$	−65.3472			−0.228487
$287$	−92.8823			−0.323632
$288$	46.1194	−	21.5639i	0.160137	−	0.0748747i
$289$	−201.431			−0.696993
$290$		0			0
$291$	15.9537	+	71.7868i	0.0548237	+	0.246690i
$292$		−	66.4044i		−	0.227412i
$293$	−312.196			−1.06552			−0.532758	−	0.846268i	$-0.678844\pi$
$293$	−312.196			−1.06552			−0.532758	+	0.846268i	$0.678844\pi$
$294$	−28.9912	+	6.44292i	−0.0986095	+	0.0219147i
$295$		0			0
$296$			108.868i			0.367798i
$297$	131.356	+	170.637i	0.442275	+	0.574537i
$298$		−	94.5643i		−	0.317330i
$299$			202.709i			0.677955i
$300$		0			0
$301$	−156.351			−0.519439
$302$	−91.1760			−0.301907
$303$	103.284	+	464.748i	0.340872	+	1.53382i
$304$	91.1918			0.299973
$305$		0			0
$306$	−107.894	+	50.4478i	−0.352596	+	0.164862i
$307$		−	155.259i		−	0.505729i	−0.967502	−	0.252864i	$-0.918627\pi$
$307$		−	155.259i		−	0.505729i	0.967502	−	0.252864i	$-0.0813727\pi$
$308$	42.2027			0.137022
$309$	−115.526	−	519.832i	−0.373871	−	1.68231i
$310$		0			0
$311$		−	338.149i		−	1.08730i	−0.839313	−	0.543649i	$-0.817042\pi$
$311$		−	338.149i		−	1.08730i	0.839313	−	0.543649i	$-0.182958\pi$
$312$	10.6651	+	47.9897i	0.0341830	+	0.153813i
$313$		−	32.5551i		−	0.104010i	−0.998647	−	0.0520050i	$-0.983439\pi$
$313$		−	32.5551i		−	0.104010i	0.998647	−	0.0520050i	$-0.0165612\pi$
$314$		−	293.106i		−	0.933460i
$315$		0			0
$316$	109.885			0.347739
$317$	156.813			0.494679			0.247340	−	0.968929i	$-0.420444\pi$
$317$	156.813			0.494679			0.247340	+	0.968929i	$0.420444\pi$
$318$	−171.951	+	38.2138i	−0.540725	+	0.120169i
$319$	124.306			0.389673
$320$		0			0
$321$	−617.902	+	137.321i	−1.92493	+	0.427791i
$322$		−	130.914i		−	0.406565i
$323$	−213.339			−0.660493
$324$	103.875	−	124.314i	0.320601	−	0.383686i
$325$		0			0
$326$		−	333.849i		−	1.02408i
$327$	288.532	−	64.1225i	0.882360	−	0.196093i
$328$		−	99.2954i		−	0.302730i
$329$		−	2.73880i		−	0.00832462i
$330$		0			0
$331$	62.7666			0.189627			0.0948136	−	0.995495i	$-0.469775\pi$
$331$	62.7666			0.189627			0.0948136	+	0.995495i	$0.469775\pi$
$332$	−157.319			−0.473851
$333$	146.727	+	313.809i	0.440620	+	0.942369i
$334$	−155.064			−0.464263
$335$		0			0
$336$	−6.88777	−	30.9929i	−0.0204993	−	0.0922407i
$337$			429.763i			1.27526i	0.770342	+	0.637631i	$0.220086\pi$
$337$			429.763i			1.27526i	−0.770342	+	0.637631i	$0.779914\pi$
$338$	191.532			0.566664
$339$	−301.143	+	66.9251i	−0.888327	+	0.197419i
$340$		0			0
$341$			204.070i			0.598446i
$342$	262.857	−	122.903i	0.768587	−	0.359366i
$343$			18.5203i			0.0539949i
$344$		−	167.146i		−	0.485890i
$345$		0			0
$346$	66.0586			0.190921
$347$	−611.203			−1.76139			−0.880695	−	0.473683i	$-0.842924\pi$
$347$	−611.203			−1.76139			−0.880695	+	0.473683i	$0.842924\pi$
$348$	−20.2875	−	91.2878i	−0.0582975	−	0.262321i
$349$	229.756			0.658327			0.329163	−	0.944273i	$-0.393233\pi$
$349$	229.756			0.658327			0.329163	+	0.944273i	$0.393233\pi$
$350$		0			0
$351$	95.4197	+	123.955i	0.271851	+	0.353148i
$352$			45.1166i			0.128172i
$353$	−434.601			−1.23117			−0.615583	−	0.788072i	$-0.711079\pi$
$353$	−434.601			−1.23117			−0.615583	+	0.788072i	$0.711079\pi$
$354$	−50.7704	−	228.452i	−0.143419	−	0.645343i
$355$		0			0
$356$			240.057i			0.674317i
$357$	16.1136	+	72.5065i	0.0451362	+	0.203099i
$358$			415.536i			1.16071i
$359$			185.884i			0.517782i	0.965907	+	0.258891i	$0.0833570\pi$
$359$			185.884i			0.517782i	−0.965907	+	0.258891i	$0.916643\pi$
$360$		0			0
$361$	158.746			0.439740
$362$	−183.320			−0.506408
$363$	168.071	−	37.3516i	0.463005	−	0.102897i
$364$	30.6570			0.0842225
$365$		0			0
$366$	−392.510	+	87.2303i	−1.07243	+	0.238334i
$367$		−	418.446i		−	1.14018i	−0.821582	−	0.570090i	$-0.806908\pi$
$367$		−	418.446i		−	1.14018i	0.821582	−	0.570090i	$-0.193092\pi$
$368$	139.953			0.380307
$369$	−133.825	−	286.215i	−0.362669	−	0.775651i
$370$		0			0
$371$			109.846i			0.296081i
$372$	149.865	−	33.3056i	0.402863	−	0.0895312i
$373$		−	597.593i		−	1.60213i	−0.598581	−	0.801063i	$-0.704268\pi$
$373$		−	597.593i		−	1.60213i	0.598581	−	0.801063i	$-0.295732\pi$
$374$		−	105.548i		−	0.282215i
$375$		0			0
$376$	2.92790			0.00778697
$377$	90.2985			0.239519
$378$	−61.6242	−	80.0528i	−0.163027	−	0.211780i
$379$	−563.466			−1.48672			−0.743358	−	0.668894i	$-0.766768\pi$
$379$	−563.466			−1.48672			−0.743358	+	0.668894i	$0.766768\pi$
$380$		0			0
$381$	102.629	+	461.797i	0.269366	+	1.21207i
$382$			10.2446i			0.0268182i
$383$	108.726			0.283881			0.141940	−	0.989875i	$-0.454666\pi$
$383$	108.726			0.283881			0.141940	+	0.989875i	$0.454666\pi$
$384$	33.1328	−	7.36333i	0.0862833	−	0.0191753i
$385$		0			0
$386$			443.598i			1.14922i
$387$	−225.270	−	481.793i	−0.582094	−	1.24494i
$388$			49.0254i			0.126354i
$389$		−	128.348i		−	0.329944i	−0.986298	−	0.164972i	$-0.947247\pi$
$389$		−	128.348i		−	0.329944i	0.986298	−	0.164972i	$-0.0527534\pi$
$390$		0			0
$391$	−327.414			−0.837375
$392$	−19.7990			−0.0505076
$393$	162.787	+	732.490i	0.414215	+	1.86384i
$394$	−133.663			−0.339245
$395$		0			0
$396$	60.8056	+	130.047i	0.153550	+	0.328401i
$397$		−	165.453i		−	0.416758i	−0.978048	−	0.208379i	$-0.933181\pi$
$397$		−	165.453i		−	0.416758i	0.978048	−	0.208379i	$-0.0668188\pi$
$398$	262.783			0.660259
$399$	−39.2567	−	176.643i	−0.0983878	−	0.442715i
$400$		0			0
$401$		−	397.048i		−	0.990144i	−0.868852	−	0.495072i	$-0.835142\pi$
$401$		−	397.048i		−	0.990144i	0.868852	−	0.495072i	$-0.164858\pi$
$402$	70.9700	+	319.344i	0.176542	+	0.794387i
$403$			148.241i			0.367844i
$404$			317.391i			0.785620i
$405$		0			0
$406$	−58.3168			−0.143638
$407$	−306.985			−0.754264
$408$	−77.5127	+	17.2262i	−0.189982	+	0.0422211i
$409$	−590.813			−1.44453			−0.722265	−	0.691616i	$-0.756899\pi$
$409$	−590.813			−1.44453			−0.722265	+	0.691616i	$0.756899\pi$
$410$		0			0
$411$	−561.977	+	124.892i	−1.36734	+	0.303874i
$412$		−	355.010i		−	0.861674i
$413$	−145.940			−0.353366
$414$	403.409	−	188.621i	0.974417	−	0.455605i
$415$		0			0
$416$			32.7737i			0.0787829i
$417$	−62.8598	+	13.9698i	−0.150743	+	0.0335007i
$418$			257.141i			0.615171i
$419$		−	275.411i		−	0.657305i	−0.944451	−	0.328653i	$-0.893405\pi$
$419$		−	275.411i		−	0.657305i	0.944451	−	0.328653i	$-0.106595\pi$
$420$		0			0
$421$	570.120			1.35420			0.677102	−	0.735890i	$-0.263236\pi$
$421$	570.120			1.35420			0.677102	+	0.735890i	$0.263236\pi$
$422$	531.333			1.25908
$423$	8.43956	−	3.94606i	0.0199517	−	0.00932875i
$424$	−117.430			−0.276959
$425$		0			0
$426$	16.5718	+	74.5679i	0.0389008	+	0.175042i
$427$			250.745i			0.587224i
$428$	−421.985			−0.985946
$429$	−135.321	+	30.0733i	−0.315433	+	0.0701010i
$430$		0			0
$431$			650.331i			1.50889i	0.656365	+	0.754444i	$0.272093\pi$
$431$			650.331i			1.50889i	−0.656365	+	0.754444i	$0.727907\pi$
$432$	85.5801	−	65.8790i	0.198102	−	0.152498i
$433$		−	635.503i		−	1.46767i	−0.679325	−	0.733837i	$-0.737727\pi$
$433$		−	635.503i		−	1.46767i	0.679325	−	0.733837i	$-0.262273\pi$
$434$		−	95.7374i		−	0.220593i
$435$		0			0
$436$	197.047			0.451943
$437$	797.659			1.82531
$438$	−30.5599	−	137.510i	−0.0697714	−	0.313950i
$439$	341.898			0.778810			0.389405	−	0.921067i	$-0.372681\pi$
$439$	341.898			0.778810			0.389405	+	0.921067i	$0.372681\pi$
$440$		0			0
$441$	−57.0698	+	26.6840i	−0.129410	+	0.0605079i
$442$		−	76.6726i		−	0.173468i
$443$	−254.231			−0.573884			−0.286942	−	0.957948i	$-0.592639\pi$
$443$	−254.231			−0.573884			−0.286942	+	0.957948i	$0.592639\pi$
$444$	50.1021	+	225.444i	0.112843	+	0.507758i
$445$		0			0
$446$			27.7337i			0.0621833i
$447$	−43.5193	−	195.824i	−0.0973586	−	0.438084i
$448$		−	21.1660i		−	0.0472456i
$449$			73.2691i			0.163183i	0.996666	+	0.0815915i	$0.0260003\pi$
$449$			73.2691i			0.163183i	−0.996666	+	0.0815915i	$0.974000\pi$
$450$		0			0
$451$	279.992			0.620825
$452$	−205.660			−0.455000
$453$	−188.807	+	41.9600i	−0.416793	+	0.0926269i
$454$	−354.874			−0.781660
$455$		0			0
$456$	188.840	−	41.9672i	0.414122	−	0.0920334i
$457$			201.124i			0.440097i	0.975489	+	0.220049i	$0.0706216\pi$
$457$			201.124i			0.440097i	−0.975489	+	0.220049i	$0.929378\pi$
$458$	−419.569			−0.916089
$459$	−200.211	+	154.121i	−0.436189	+	0.335776i
$460$		0			0
$461$		−	500.367i		−	1.08539i	−0.839929	−	0.542697i	$-0.817403\pi$
$461$		−	500.367i		−	1.08539i	0.839929	−	0.542697i	$-0.182597\pi$
$462$	87.3933	−	19.4220i	0.189163	−	0.0420391i
$463$			601.585i			1.29932i	0.760225	+	0.649660i	$0.225089\pi$
$463$			601.585i			1.29932i	−0.760225	+	0.649660i	$0.774911\pi$
$464$		−	62.3433i		−	0.134361i
$465$		0			0
$466$	−222.714			−0.477927
$467$	−271.025			−0.580353			−0.290176	−	0.956973i	$-0.593714\pi$
$467$	−271.025			−0.580353			−0.290176	+	0.956973i	$0.593714\pi$
$468$	44.1706	+	94.4690i	0.0943816	+	0.201857i
$469$	204.004			0.434977
$470$		0			0
$471$	−134.890	−	606.964i	−0.286391	−	1.28867i
$472$		−	156.017i		−	0.330544i
$473$	471.317			0.996442
$474$	227.551	−	50.5702i	0.480065	−	0.106688i
$475$		0			0
$476$			49.5170i			0.104027i
$477$	−338.489	+	158.266i	−0.709620	+	0.331795i
$478$			111.407i			0.233069i
$479$			203.003i			0.423807i	0.977291	+	0.211903i	$0.0679662\pi$
$479$			203.003i			0.423807i	−0.977291	+	0.211903i	$0.932034\pi$
$480$		0			0
$481$	−223.001			−0.463620
$482$	−209.796			−0.435262
$483$	−60.2477	−	271.096i	−0.124736	−	0.561276i
$484$	114.781			0.237150
$485$		0			0
$486$	157.893	−	305.234i	0.324883	−	0.628053i
$487$			795.875i			1.63424i	0.576468	+	0.817120i	$0.304431\pi$
$487$			795.875i			1.63424i	−0.576468	+	0.817120i	$0.695569\pi$
$488$	−268.057			−0.549298
$489$	−153.640	−	691.334i	−0.314193	−	1.41377i
$490$		0			0
$491$		−	41.1374i		−	0.0837830i	−0.999122	−	0.0418915i	$-0.986662\pi$
$491$		−	41.1374i		−	0.0837830i	0.999122	−	0.0418915i	$-0.0133384\pi$
$492$	−45.6966	−	205.621i	−0.0928792	−	0.417928i
$493$			145.849i			0.295841i
$494$			186.793i			0.378124i
$495$		0			0
$496$	102.348			0.206346
$497$	47.6357			0.0958466
$498$	−325.775	+	72.3994i	−0.654167	+	0.145380i
$499$	−590.508			−1.18338			−0.591692	−	0.806164i	$-0.701540\pi$
$499$	−590.508			−1.18338			−0.591692	+	0.806164i	$0.701540\pi$
$500$		0			0
$501$	−321.106	+	71.3618i	−0.640931	+	0.142439i
$502$		−	315.676i		−	0.628837i
$503$	276.575			0.549850			0.274925	−	0.961466i	$-0.411347\pi$
$503$	276.575			0.549850			0.274925	+	0.961466i	$0.411347\pi$
$504$	−28.5264	−	61.0102i	−0.0565999	−	0.121052i
$505$		0			0
$506$			394.637i			0.779916i
$507$	396.625	−	88.1448i	0.782298	−	0.173856i
$508$			315.376i			0.620819i
$509$			311.610i			0.612201i	0.951999	+	0.306100i	$0.0990243\pi$
$509$			311.610i			0.612201i	−0.951999	+	0.306100i	$0.900976\pi$
$510$		0			0
$511$	−87.8448			−0.171908
$512$	22.6274			0.0441942
$513$	487.762	−	375.477i	0.950804	−	0.731923i
$514$	509.019			0.990309
$515$		0			0
$516$	−76.9221	−	346.126i	−0.149074	−	0.670788i
$517$			8.25606i			0.0159692i
$518$	144.019			0.278029
$519$	136.794	−	30.4007i	0.263572	−	0.0585756i
$520$		0			0
$521$		−	435.399i		−	0.835698i	−0.908516	−	0.417849i	$-0.862784\pi$
$521$		−	435.399i		−	0.835698i	0.908516	−	0.417849i	$-0.137216\pi$
$522$	−84.0229	−	179.702i	−0.160963	−	0.344257i
$523$		−	619.746i		−	1.18498i	−0.805577	−	0.592491i	$-0.798144\pi$
$523$		−	619.746i		−	1.18498i	0.805577	−	0.592491i	$-0.201856\pi$
$524$			500.241i			0.954658i
$525$		0			0
$526$	323.009			0.614085
$527$	−239.438			−0.454341
$528$	20.7630	+	93.4274i	0.0393239	+	0.176946i
$529$	695.175			1.31413
$530$		0			0
$531$	−210.271	−	449.712i	−0.395990	−	0.846916i
$532$		−	120.635i		−	0.226758i
$533$	203.392			0.381599
$534$	110.476	+	497.110i	0.206884	+	0.930917i
$535$		0			0
$536$			218.090i			0.406884i
$537$	191.233	+	860.491i	0.356114	+	1.60240i
$538$		−	400.969i		−	0.745295i
$539$		−	55.8289i		−	0.103579i
$540$		0			0
$541$	709.366			1.31121			0.655606	−	0.755103i	$-0.272413\pi$
$541$	709.366			1.31121			0.655606	+	0.755103i	$0.272413\pi$
$542$	−411.238			−0.758742
$543$	−379.618	+	84.3652i	−0.699112	+	0.155369i
$544$	−52.9359			−0.0973086
$545$		0			0
$546$	63.4845	−	14.1086i	0.116272	−	0.0258399i
$547$		−	306.448i		−	0.560234i	−0.959966	−	0.280117i	$-0.909627\pi$
$547$		−	306.448i		−	0.560234i	0.959966	−	0.280117i	$-0.0903733\pi$
$548$	−383.792			−0.700350
$549$	−772.665	+	361.273i	−1.40740	+	0.658056i
$550$		0			0
$551$		−	355.325i		−	0.644873i
$552$	289.814	−	64.4075i	0.525026	−	0.116680i
$553$		−	145.365i		−	0.262866i
$554$		−	378.260i		−	0.682780i
$555$		0			0
$556$	−42.9289			−0.0772103
$557$	259.701			0.466250			0.233125	−	0.972447i	$-0.425105\pi$
$557$	259.701			0.466250			0.233125	+	0.972447i	$0.425105\pi$
$558$	295.013	−	137.938i	0.528697	−	0.247201i
$559$	342.375			0.612478
$560$		0			0
$561$	−48.5742	−	218.569i	−0.0865851	−	0.389607i
$562$			300.787i			0.535209i
$563$	−1066.78			−1.89481			−0.947407	−	0.320032i	$-0.896306\pi$
$563$	−1066.78			−1.89481			−0.947407	+	0.320032i	$0.896306\pi$
$564$	6.06309	−	1.34744i	0.0107502	−	0.00238909i
$565$		0			0
$566$			353.195i			0.624019i
$567$	−164.452	−	137.413i	−0.290039	−	0.242352i
$568$			50.9248i			0.0896563i
$569$		−	294.913i		−	0.518301i	−0.965837	−	0.259150i	$-0.916557\pi$
$569$		−	294.913i		−	0.518301i	0.965837	−	0.259150i	$-0.0834425\pi$
$570$		0			0
$571$	183.465			0.321304			0.160652	−	0.987011i	$-0.448640\pi$
$571$	183.465			0.321304			0.160652	+	0.987011i	$0.448640\pi$
$572$	−92.4149			−0.161564
$573$	4.71463	+	21.2144i	0.00822798	+	0.0370234i
$574$	−131.355			−0.228842
$575$		0			0
$576$	65.2227	−	30.4960i	0.113234	−	0.0529444i
$577$			740.634i			1.28359i	0.766874	+	0.641797i	$0.221811\pi$
$577$			740.634i			1.28359i	−0.766874	+	0.641797i	$0.778189\pi$
$578$	−284.867			−0.492849
$579$	204.148	+	918.603i	0.352587	+	1.58653i
$580$		0			0
$581$			208.113i			0.358198i
$582$	22.5619	+	101.522i	0.0387662	+	0.174436i
$583$		−	331.129i		−	0.567974i
$584$		−	93.9101i		−	0.160805i
$585$		0			0
$586$	−441.512			−0.753433
$587$	−694.040			−1.18235			−0.591175	−	0.806543i	$-0.701336\pi$
$587$	−694.040			−1.18235			−0.591175	+	0.806543i	$0.701336\pi$
$588$	−40.9997	+	9.11166i	−0.0697274	+	0.0154960i
$589$	583.329			0.990371
$590$		0			0
$591$	−276.788	+	61.5126i	−0.468339	+	0.104082i
$592$			153.963i			0.260073i
$593$	428.653			0.722855			0.361427	−	0.932400i	$-0.382290\pi$
$593$	428.653			0.722855			0.361427	+	0.932400i	$0.382290\pi$
$594$	185.765	+	241.318i	0.312736	+	0.406259i
$595$		0			0
$596$		−	133.734i		−	0.224386i
$597$	544.171	−	120.935i	0.911509	−	0.202571i
$598$			286.673i			0.479387i
$599$			1068.82i			1.78433i	0.451705	+	0.892167i	$0.350816\pi$
$599$			1068.82i			1.78433i	−0.451705	+	0.892167i	$0.649184\pi$
$600$		0			0
$601$	259.767			0.432224			0.216112	−	0.976369i	$-0.430662\pi$
$601$	259.767			0.432224			0.216112	+	0.976369i	$0.430662\pi$
$602$	−221.114			−0.367299
$603$	293.929	+	628.636i	0.487445	+	1.04251i
$604$	−128.942			−0.213481
$605$		0			0
$606$	146.066	+	657.252i	0.241033	+	1.08457i
$607$		−	1147.06i		−	1.88972i	−0.327479	−	0.944858i	$-0.606199\pi$
$607$		−	1147.06i		−	1.88972i	0.327479	−	0.944858i	$-0.393801\pi$
$608$	128.965			0.212113
$609$	−120.762	+	26.8379i	−0.198296	+	0.0440688i
$610$		0			0
$611$			5.99739i			0.00981569i
$612$	−152.586	+	71.3440i	−0.249323	+	0.116575i
$613$			166.678i			0.271905i	0.990715	+	0.135952i	$0.0434094\pi$
$613$			166.678i			0.271905i	−0.990715	+	0.135952i	$0.956591\pi$
$614$		−	219.569i		−	0.357604i
$615$		0			0
$616$	59.6837			0.0968890
$617$	319.900			0.518477			0.259238	−	0.965813i	$-0.416528\pi$
$617$	319.900			0.518477			0.259238	+	0.965813i	$0.416528\pi$
$618$	−163.379	−	735.154i	−0.264367	−	1.18957i
$619$	917.131			1.48163			0.740817	−	0.671707i	$-0.234439\pi$
$619$	917.131			1.48163			0.740817	+	0.671707i	$0.234439\pi$
$620$		0			0
$621$	748.574	−	576.247i	1.20543	−	0.927935i
$622$		−	478.216i		−	0.768835i
$623$	317.565			0.509736
$624$	15.0827	+	67.8678i	0.0241710	+	0.108762i
$625$		0			0
$626$		−	46.0399i		−	0.0735461i
$627$	118.339	+	532.488i	0.188738	+	0.849263i
$628$		−	414.515i		−	0.660056i
$629$		−	360.190i		−	0.572639i
$630$		0			0
$631$	695.889			1.10283			0.551417	−	0.834229i	$-0.314087\pi$
$631$	695.889			1.10283			0.551417	+	0.834229i	$0.314087\pi$
$632$	155.402			0.245889
$633$	1100.28	−	244.524i	1.73820	−	0.386294i
$634$	221.767			0.349791
$635$		0			0
$636$	−243.175	+	54.0425i	−0.382350	+	0.0849725i
$637$		−	40.5554i		−	0.0636662i
$638$	175.795			0.275541
$639$	68.6335	+	146.789i	0.107408	+	0.229716i
$640$		0			0
$641$			75.7558i			0.118184i	0.998253	+	0.0590919i	$0.0188205\pi$
$641$			75.7558i			0.118184i	−0.998253	+	0.0590919i	$0.981180\pi$
$642$	−873.846	+	194.201i	−1.36113	+	0.302494i
$643$		−	1173.40i		−	1.82488i	−0.409215	−	0.912438i	$-0.634197\pi$
$643$		−	1173.40i		−	1.82488i	0.409215	−	0.912438i	$-0.365803\pi$
$644$		−	185.140i		−	0.287485i
$645$		0			0
$646$	−301.707			−0.467039
$647$	322.830			0.498964			0.249482	−	0.968379i	$-0.419740\pi$
$647$	322.830			0.498964			0.249482	+	0.968379i	$0.419740\pi$
$648$	146.901	−	175.807i	0.226699	−	0.271307i
$649$	439.934			0.677864
$650$		0			0
$651$	−44.0592	−	198.253i	−0.0676792	−	0.304536i
$652$		−	472.134i		−	0.724132i
$653$	1056.82			1.61841			0.809206	−	0.587526i	$-0.199898\pi$
$653$	1056.82			1.61841			0.809206	+	0.587526i	$0.199898\pi$
$654$	408.045	−	90.6828i	0.623923	−	0.138659i
$655$		0			0
$656$		−	140.425i		−	0.214062i
$657$	−126.567	−	270.692i	−0.192643	−	0.412012i
$658$		−	3.87325i		−	0.00588640i
$659$			808.670i			1.22712i	0.789649	+	0.613559i	$0.210263\pi$
$659$			808.670i			1.22712i	−0.789649	+	0.613559i	$0.789737\pi$
$660$		0			0
$661$	1068.86			1.61703			0.808515	−	0.588476i	$-0.200272\pi$
$661$	1068.86			1.61703			0.808515	+	0.588476i	$0.200272\pi$
$662$	88.7654			0.134087
$663$	−35.2854	−	158.774i	−0.0532208	−	0.239478i
$664$	−222.482			−0.335064
$665$		0			0
$666$	207.503	+	443.793i	0.311566	+	0.666355i
$667$		−	545.320i		−	0.817572i
$668$	−219.294			−0.328284
$669$	12.7633	+	57.4310i	0.0190782	+	0.0858460i
$670$		0			0
$671$		−	755.865i		−	1.12647i
$672$	−9.74078	−	43.8306i	−0.0144952	−	0.0652240i
$673$			1159.59i			1.72302i	0.507744	+	0.861508i	$0.330479\pi$
$673$			1159.59i			1.72302i	−0.507744	+	0.861508i	$0.669521\pi$
$674$			607.777i			0.901747i
$675$		0			0
$676$	270.868			0.400692
$677$	−202.423			−0.298999			−0.149500	−	0.988762i	$-0.547766\pi$
$677$	−202.423			−0.298999			−0.149500	+	0.988762i	$0.547766\pi$
$678$	−425.880	+	94.6464i	−0.628142	+	0.139596i
$679$	64.8546			0.0955148
$680$		0			0
$681$	−734.872	+	163.316i	−1.07911	+	0.239818i
$682$			288.599i			0.423165i
$683$	432.740			0.633587			0.316794	−	0.948494i	$-0.397394\pi$
$683$	432.740			0.633587			0.316794	+	0.948494i	$0.397394\pi$
$684$	371.736	−	173.811i	0.543473	−	0.254110i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	−868.843	+	193.089i	−1.26469	+	0.281061i
$688$		−	236.381i		−	0.343576i
$689$		−	240.539i		−	0.349114i
$690$		0			0
$691$	−507.481			−0.734415			−0.367208	−	0.930139i	$-0.619686\pi$
$691$	−507.481			−0.734415			−0.367208	+	0.930139i	$0.619686\pi$
$692$	93.4210			0.135001
$693$	172.036	−	80.4383i	0.248248	−	0.116073i
$694$	−864.371			−1.24549
$695$		0			0
$696$	−28.6909	−	129.100i	−0.0412226	−	0.185489i
$697$			328.518i			0.471331i
$698$	324.924			0.465507
$699$	−461.196	+	102.495i	−0.659794	+	0.146631i
$700$		0			0
$701$			465.228i			0.663663i	0.943339	+	0.331831i	$0.107667\pi$
$701$			465.228i			0.663663i	−0.943339	+	0.331831i	$0.892333\pi$
$702$	134.944	+	175.299i	0.192228	+	0.249713i
$703$			877.510i			1.24824i
$704$			63.8045i			0.0906314i
$705$		0			0
$706$	−614.619			−0.870566
$707$	419.868			0.593873
$708$	−71.8002	−	323.079i	−0.101413	−	0.456327i
$709$	902.795			1.27334			0.636668	−	0.771138i	$-0.280312\pi$
$709$	902.795			1.27334			0.636668	+	0.771138i	$0.280312\pi$
$710$		0			0
$711$	447.939	−	209.442i	0.630013	−	0.294573i
$712$			339.492i			0.476814i
$713$	895.240			1.25560
$714$	22.7881	+	102.540i	0.0319161	+	0.143613i
$715$		0			0
$716$			587.656i			0.820749i
$717$	51.2703	+	230.701i	0.0715067	+	0.321759i
$718$			262.879i			0.366127i
$719$		−	1105.81i		−	1.53798i	−0.639262	−	0.768989i	$-0.720760\pi$
$719$		−	1105.81i		−	1.53798i	0.639262	−	0.768989i	$-0.279240\pi$
$720$		0			0
$721$	−469.634			−0.651365
$722$	224.501			0.310943
$723$	−434.446	+	96.5500i	−0.600893	+	0.133541i
$724$	−259.253			−0.358084
$725$		0			0
$726$	237.688	−	52.8231i	0.327394	−	0.0727591i
$727$		−	215.564i		−	0.296512i	−0.988949	−	0.148256i	$-0.952634\pi$
$727$		−	215.564i		−	0.296512i	0.988949	−	0.148256i	$-0.0473660\pi$
$728$	43.3555			0.0595543
$729$	186.494	−	704.742i	0.255822	−	0.966724i
$730$		0			0
$731$			553.002i			0.756501i
$732$	−555.093	+	123.362i	−0.758323	+	0.168528i
$733$		−	1068.10i		−	1.45716i	−0.684963	−	0.728578i	$-0.740181\pi$
$733$		−	1068.10i		−	1.45716i	0.684963	−	0.728578i	$-0.259819\pi$
$734$		−	591.772i		−	0.806229i
$735$		0			0
$736$	197.923			0.268917
$737$	−614.967			−0.834419
$738$	−189.257	−	404.769i	−0.256446	−	0.548468i
$739$	156.720			0.212071			0.106035	−	0.994362i	$-0.466184\pi$
$739$	156.720			0.212071			0.106035	+	0.994362i	$0.466184\pi$
$740$		0			0
$741$	85.9638	+	386.811i	0.116011	+	0.522012i
$742$			155.346i			0.209361i
$743$	423.464			0.569938			0.284969	−	0.958537i	$-0.408017\pi$
$743$	423.464			0.569938			0.284969	+	0.958537i	$0.408017\pi$
$744$	211.941	−	47.1012i	0.284867	−	0.0633081i
$745$		0			0
$746$		−	845.124i		−	1.13287i
$747$	−641.296	+	299.849i	−0.858496	+	0.401404i
$748$		−	149.268i		−	0.199556i
$749$			558.234i			0.745305i
$750$		0			0
$751$	−1305.05			−1.73776			−0.868878	−	0.495026i	$-0.835158\pi$
$751$	−1305.05			−1.73776			−0.868878	+	0.495026i	$0.835158\pi$
$752$	4.14068			0.00550622
$753$	−145.277	−	653.702i	−0.192931	−	0.868130i
$754$	127.701			0.169365
$755$		0			0
$756$	−87.1498	−	113.212i	−0.115277	−	0.149751i
$757$			59.6912i			0.0788523i	0.999222	+	0.0394261i	$0.0125530\pi$
$757$			59.6912i			0.0788523i	−0.999222	+	0.0394261i	$0.987447\pi$
$758$	−796.861			−1.05127
$759$	181.615	+	817.214i	0.239282	+	1.07670i
$760$		0			0
$761$		−	899.617i		−	1.18215i	−0.806616	−	0.591075i	$-0.798704\pi$
$761$		−	899.617i		−	1.18215i	0.806616	−	0.591075i	$-0.201296\pi$
$762$	145.139	+	653.080i	0.190471	+	0.857060i
$763$		−	260.669i		−	0.341637i
$764$			14.4880i			0.0189633i
$765$		0			0
$766$	153.762			0.200734
$767$	319.578			0.416660
$768$	46.8568	−	10.4133i	0.0610115	−	0.0135590i
$769$	268.385			0.349005			0.174503	−	0.984657i	$-0.444168\pi$
$769$	268.385			0.349005			0.174503	+	0.984657i	$0.444168\pi$
$770$		0			0
$771$	1054.08	−	234.255i	1.36715	−	0.303832i
$772$			627.343i			0.812620i
$773$	−80.8488			−0.104591			−0.0522955	−	0.998632i	$-0.516654\pi$
$773$	−80.8488			−0.104591			−0.0522955	+	0.998632i	$0.516654\pi$
$774$	−318.581	−	681.358i	−0.411603	−	0.880307i
$775$		0			0
$776$			69.3324i			0.0893459i
$777$	298.235	−	66.2789i	0.383829	−	0.0853010i
$778$		−	181.512i		−	0.233306i
$779$		−	800.350i		−	1.02741i
$780$		0			0
$781$	−143.597			−0.183863
$782$	−463.033			−0.592113
$783$	−256.695	−	333.459i	−0.327835	−	0.425874i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	230.215	+	1035.90i	0.292894	+	1.31794i
$787$			592.703i			0.753117i	0.926393	+	0.376559i	$0.122893\pi$
$787$			592.703i			0.753117i	−0.926393	+	0.376559i	$0.877107\pi$
$788$	−189.027			−0.239882
$789$	668.886	−	148.651i	0.847764	−	0.188405i
$790$		0			0
$791$			272.062i			0.343948i
$792$	85.9922	+	183.914i	0.108576	+	0.232215i
$793$		−	549.077i		−	0.692405i
$794$		−	233.986i		−	0.294693i
$795$		0			0
$796$	371.632			0.466874
$797$	463.874			0.582025			0.291012	−	0.956719i	$-0.406008\pi$
$797$	463.874			0.582025			0.291012	+	0.956719i	$0.406008\pi$
$798$	−55.5174	−	249.812i	−0.0695707	−	0.313047i
$799$	−9.68693			−0.0121238
$800$		0			0
$801$	457.548	+	978.572i	0.571221	+	1.22169i
$802$		−	561.510i		−	0.700138i
$803$	264.806			0.329771
$804$	100.367	+	451.620i	0.124834	+	0.561717i
$805$		0			0
$806$			209.644i			0.260105i
$807$	−184.529	−	830.326i	−0.228661	−	1.02890i
$808$			448.858i			0.555518i
$809$		−	454.905i		−	0.562305i	−0.959663	−	0.281152i	$-0.909283\pi$
$809$		−	454.905i		−	0.562305i	0.959663	−	0.281152i	$-0.0907166\pi$
$810$		0			0
$811$	349.822			0.431346			0.215673	−	0.976466i	$-0.430805\pi$
$811$	349.822			0.431346			0.215673	+	0.976466i	$0.430805\pi$
$812$	−82.4725			−0.101567
$813$	−851.591	+	189.255i	−1.04747	+	0.232786i
$814$	−434.143			−0.533345
$815$		0			0
$816$	−109.620	+	24.3615i	−0.134338	+	0.0298548i
$817$		−	1347.25i		−	1.64902i
$818$	−835.536			−1.02144
$819$	124.971	−	58.4322i	0.152589	−	0.0713458i
$820$		0			0
$821$		−	779.459i		−	0.949402i	−0.880147	−	0.474701i	$-0.842556\pi$
$821$		−	779.459i		−	0.949402i	0.880147	−	0.474701i	$-0.157444\pi$
$822$	−794.755	+	176.624i	−0.966856	+	0.214871i
$823$			931.372i			1.13168i	0.824516	+	0.565839i	$0.191448\pi$
$823$			931.372i			1.13168i	−0.824516	+	0.565839i	$0.808552\pi$
$824$		−	502.060i		−	0.609296i
$825$		0			0
$826$	−206.391			−0.249868
$827$	−197.854			−0.239243			−0.119621	−	0.992820i	$-0.538168\pi$
$827$	−197.854			−0.239243			−0.119621	+	0.992820i	$0.538168\pi$
$828$	570.506	−	266.750i	0.689017	−	0.322162i
$829$	767.502			0.925816			0.462908	−	0.886406i	$-0.346806\pi$
$829$	767.502			0.925816			0.462908	+	0.886406i	$0.346806\pi$
$830$		0			0
$831$	−174.078	−	783.300i	−0.209481	−	0.942599i
$832$			46.3490i			0.0557080i
$833$	65.5048			0.0786372
$834$	−88.8972	+	19.7563i	−0.106591	+	0.0236886i
$835$		0			0
$836$			363.653i			0.434991i
$837$	547.432	−	421.410i	0.654041	−	0.503477i
$838$		−	389.490i		−	0.464785i
$839$			789.441i			0.940931i	0.882418	+	0.470466i	$0.155914\pi$
$839$			789.441i			0.940931i	−0.882418	+	0.470466i	$0.844086\pi$
$840$		0			0
$841$	598.082			0.711156
$842$	806.271			0.957566
$843$	138.425	+	622.870i	0.164205	+	0.738874i
$844$	751.418			0.890306
$845$		0			0
$846$	11.9353	−	5.58057i	0.0141080	−	0.00659642i
$847$		−	151.841i		−	0.179269i
$848$	−166.072			−0.195839
$849$	162.543	+	731.395i	0.191452	+	0.861478i
$850$		0			0
$851$			1346.72i			1.58252i
$852$	23.4360	+	105.455i	0.0275070	+	0.123773i
$853$			167.784i			0.196699i	0.995152	+	0.0983493i	$0.0313563\pi$
$853$			167.784i			0.196699i	−0.995152	+	0.0983493i	$0.968644\pi$
$854$			354.606i			0.415230i
$855$		0			0
$856$	−596.777			−0.697169
$857$	873.473			1.01922			0.509611	−	0.860405i	$-0.329789\pi$
$857$	873.473			1.01922			0.509611	+	0.860405i	$0.329789\pi$
$858$	−191.373	+	42.5301i	−0.223045	+	0.0495689i
$859$	−480.534			−0.559411			−0.279705	−	0.960086i	$-0.590237\pi$
$859$	−480.534			−0.559411			−0.279705	+	0.960086i	$0.590237\pi$
$860$		0			0
$861$	−272.011	+	60.4509i	−0.315924	+	0.0702101i
$862$			919.706i			1.06694i
$863$	−263.159			−0.304936			−0.152468	−	0.988308i	$-0.548722\pi$
$863$	−263.159			−0.304936			−0.152468	+	0.988308i	$0.548722\pi$
$864$	121.029	−	93.1670i	0.140079	−	0.107832i
$865$		0			0
$866$		−	898.737i		−	1.03780i
$867$	−589.901	+	131.098i	−0.680394	+	0.151209i
$868$		−	135.393i		−	0.155983i
$869$			438.199i			0.504257i
$870$		0			0
$871$	−446.726			−0.512888
$872$	278.667			0.319572
$873$	93.4424	+	199.848i	0.107036	+	0.228921i
$874$	1128.06			1.29069
$875$		0			0
$876$	−43.2182	−	194.469i	−0.0493358	−	0.221996i
$877$		−	982.305i		−	1.12007i	−0.828468	−	0.560037i	$-0.810787\pi$
$877$		−	982.305i		−	1.12007i	0.828468	−	0.560037i	$-0.189213\pi$
$878$	483.517			0.550702
$879$	−914.282	+	203.187i	−1.04014	+	0.231158i
$880$		0			0
$881$			651.840i			0.739886i	0.929054	+	0.369943i	$0.120623\pi$
$881$			651.840i			0.739886i	−0.929054	+	0.369943i	$0.879377\pi$
$882$	−80.7089	+	37.7368i	−0.0915067	+	0.0427855i
$883$		−	811.043i		−	0.918509i	−0.888305	−	0.459254i	$-0.848117\pi$
$883$		−	811.043i		−	0.918509i	0.888305	−	0.459254i	$-0.151883\pi$
$884$		−	108.432i		−	0.122660i
$885$		0			0
$886$	−359.536			−0.405797
$887$	795.521			0.896867			0.448433	−	0.893816i	$-0.351982\pi$
$887$	795.521			0.896867			0.448433	+	0.893816i	$0.351982\pi$
$888$	70.8551	+	318.826i	0.0797918	+	0.359039i
$889$	417.203			0.469295
$890$		0			0
$891$	495.738	+	414.230i	0.556384	+	0.464904i
$892$			39.2214i			0.0439702i
$893$	23.5997			0.0264275
$894$	−61.5456	−	276.937i	−0.0688429	−	0.309772i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	131.929	+	593.643i	0.147079	+	0.661809i
$898$			103.618i			0.115388i
$899$		−	398.793i		−	0.443596i
$900$		0			0
$901$	388.518			0.431207
$902$	395.968			0.438989
$903$	−457.882	+	101.758i	−0.507068	+	0.112689i
$904$	−290.847			−0.321733
$905$		0			0
$906$	−267.014	+	59.3404i	−0.294717	+	0.0654971i
$907$			855.003i			0.942672i	0.881954	+	0.471336i	$0.156228\pi$
$907$			855.003i			0.942672i	−0.881954	+	0.471336i	$0.843772\pi$
$908$	−501.867			−0.552717
$909$	604.946	+	1293.82i	0.665507	+	1.42334i
$910$		0			0
$911$		−	1234.06i		−	1.35462i	−0.735696	−	0.677312i	$-0.763145\pi$
$911$		−	1234.06i		−	1.35462i	0.735696	−	0.677312i	$-0.236855\pi$
$912$	267.060	−	59.3506i	0.292829	−	0.0650774i
$913$		−	627.352i		−	0.687133i
$914$			284.433i			0.311196i
$915$		0			0
$916$	−593.360			−0.647773
$917$	661.756			0.721653
$918$	−283.141	+	217.960i	−0.308432	+	0.237429i
$919$	1390.69			1.51326			0.756632	−	0.653842i	$-0.226844\pi$
$919$	1390.69			1.51326			0.756632	+	0.653842i	$0.226844\pi$
$920$		0			0
$921$	−101.048	−	454.683i	−0.109715	−	0.493684i
$922$		−	707.625i		−	0.767490i
$923$	−104.312			−0.113014
$924$	123.593	−	27.4669i	0.133758	−	0.0297261i
$925$		0			0
$926$			850.770i			0.918758i
$927$	−676.648	−	1447.17i	−0.729933	−	1.56113i
$928$		−	88.1668i		−	0.0950073i
$929$		−	934.368i		−	1.00578i	−0.864351	−	0.502889i	$-0.832270\pi$
$929$		−	934.368i		−	1.00578i	0.864351	−	0.502889i	$-0.167730\pi$
$930$		0			0
$931$	−159.586			−0.171413
$932$	−314.965			−0.337946
$933$	−220.079	−	990.288i	−0.235883	−	1.06140i
$934$	−383.287			−0.410372
$935$		0			0
$936$	62.4666	+	133.599i	0.0667378	+	0.142734i
$937$			229.679i			0.245122i	0.992461	+	0.122561i	$0.0391107\pi$
$937$			229.679i			0.245122i	−0.992461	+	0.122561i	$0.960889\pi$
$938$	288.506			0.307575
$939$	−21.1879	−	95.3393i	−0.0225644	−	0.101533i
$940$		0			0
$941$			688.683i			0.731863i	0.930642	+	0.365932i	$0.119250\pi$
$941$			688.683i			0.731863i	−0.930642	+	0.365932i	$0.880750\pi$
$942$	−190.763	−	858.377i	−0.202509	−	0.911228i
$943$		−	1228.30i		−	1.30255i
$944$		−	220.641i		−	0.233730i
$945$		0			0
$946$	666.543			0.704591
$947$	897.803			0.948049			0.474025	−	0.880512i	$-0.342801\pi$
$947$	897.803			0.948049			0.474025	+	0.880512i	$0.342801\pi$
$948$	321.805	−	71.5171i	0.339457	−	0.0754400i
$949$	192.361			0.202699
$950$		0			0
$951$	459.236	−	102.059i	0.482898	−	0.107318i
$952$			70.0275i			0.0735584i
$953$	−809.558			−0.849483			−0.424742	−	0.905315i	$-0.639635\pi$
$953$	−809.558			−0.849483			−0.424742	+	0.905315i	$0.639635\pi$
$954$	−478.695	+	223.822i	−0.501777	+	0.234614i
$955$		0			0
$956$			157.553i			0.164804i
$957$	364.036	−	80.9023i	0.380393	−	0.0845374i
$958$			287.090i			0.299677i
$959$			507.709i			0.529415i
$960$		0			0
$961$	−306.310			−0.318741
$962$	−315.371			−0.327829
$963$	−1720.19	+	804.302i	−1.78628	+	0.835205i
$964$	−296.697			−0.307777
$965$		0			0
$966$	−85.2031	−	383.388i	−0.0882019	−	0.396882i
$967$			952.817i			0.985333i	0.870218	+	0.492667i	$0.163978\pi$
$967$			952.817i			0.985333i	−0.870218	+	0.492667i	$0.836022\pi$
$968$	162.325			0.167691
$969$	−624.775	+	138.848i	−0.644762	+	0.143290i
$970$		0			0
$971$			755.094i			0.777646i	0.921313	+	0.388823i	$0.127118\pi$
$971$			755.094i			0.777646i	−0.921313	+	0.388823i	$0.872882\pi$
$972$	223.295	−	431.666i	0.229727	−	0.444101i
$973$			56.7897i			0.0583655i
$974$			1125.54i			1.15558i
$975$		0			0
$976$	−379.090			−0.388412
$977$	1865.83			1.90975			0.954876	−	0.297006i	$-0.0959881\pi$
$977$	1865.83			1.90975			0.954876	+	0.297006i	$0.0959881\pi$
$978$	−217.280	−	977.694i	−0.222168	−	0.999687i
$979$	−957.295			−0.977829
$980$		0			0
$981$	803.247	−	375.572i	0.818804	−	0.382846i
$982$		−	58.1771i		−	0.0592435i
$983$	1469.42			1.49483			0.747417	−	0.664356i	$-0.231294\pi$
$983$	1469.42			1.49483			0.747417	+	0.664356i	$0.231294\pi$
$984$	−64.6247	−	290.792i	−0.0656755	−	0.295520i
$985$		0			0
$986$			206.262i			0.209191i
$987$	−1.78250	−	8.02072i	−0.00180598	−	0.00812636i
$988$			264.166i			0.267374i
$989$		−	2067.63i		−	2.09063i
$990$		0			0
$991$	1075.76			1.08553			0.542764	−	0.839885i	$-0.317378\pi$
$991$	1075.76			1.08553			0.542764	+	0.839885i	$0.317378\pi$
$992$	144.741			0.145909
$993$	183.815	−	40.8506i	0.185111	−	0.0411385i
$994$	67.3671			0.0677738
$995$		0			0
$996$	−460.716	+	102.388i	−0.462566	+	0.102799i
$997$			1114.55i			1.11791i	0.829199	+	0.558953i	$0.188797\pi$
$997$			1114.55i			1.11791i	−0.829199	+	0.558953i	$0.811203\pi$
$998$	−835.105			−0.836779
$999$	633.934	+	823.511i	0.634568	+	0.824335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.31		32
3.2	odd	2	inner	1050.3.c.c.449.1		32
5.2	odd	4		1050.3.e.d.701.11		16
5.3	odd	4		210.3.e.a.71.6	✓	16
5.4	even	2	inner	1050.3.c.c.449.2		32
15.2	even	4		1050.3.e.d.701.3		16
15.8	even	4		210.3.e.a.71.14	yes	16
15.14	odd	2	inner	1050.3.c.c.449.32		32
20.3	even	4		1680.3.l.c.1121.5		16
60.23	odd	4		1680.3.l.c.1121.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.6	✓	16	5.3	odd	4
210.3.e.a.71.14	yes	16	15.8	even	4
1050.3.c.c.449.1		32	3.2	odd	2	inner
1050.3.c.c.449.2		32	5.4	even	2	inner
1050.3.c.c.449.31		32	1.1	even	1	trivial
1050.3.c.c.449.32		32	15.14	odd	2	inner
1050.3.e.d.701.3		16	15.2	even	4
1050.3.e.d.701.11		16	5.2	odd	4
1680.3.l.c.1121.5		16	20.3	even	4
1680.3.l.c.1121.6		16	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(2.92855 - 0.650833i) q^{3} +2.00000 q^{4} +(4.14160 - 0.920417i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(8.15283 - 3.81200i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(2.92855 - 0.650833i) q^{3} +2.00000 q^{4} +(4.14160 - 0.920417i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(8.15283 - 3.81200i) q^{9} +7.97556i q^{11} +(5.85710 - 1.30167i) q^{12} +5.79363i q^{13} -3.74166i q^{14} +4.00000 q^{16} -9.35782 q^{17} +(11.5298 - 5.39098i) q^{18} +22.7979 q^{19} +(-1.72194 - 7.74822i) q^{21} +11.2792i q^{22} +34.9882 q^{23} +(8.28320 - 1.84083i) q^{24} +8.19343i q^{26} +(21.3950 - 16.4698i) q^{27} -5.29150i q^{28} -15.5858i q^{29} +25.5869 q^{31} +5.65685 q^{32} +(5.19076 + 23.3569i) q^{33} -13.2340 q^{34} +(16.3057 - 7.62399i) q^{36} +38.4908i q^{37} +32.2412 q^{38} +(3.77068 + 16.9669i) q^{39} -35.1062i q^{41} +(-2.43519 - 10.9576i) q^{42} -59.0951i q^{43} +15.9511i q^{44} +49.4808 q^{46} +1.03517 q^{47} +(11.7142 - 2.60333i) q^{48} -7.00000 q^{49} +(-27.4049 + 6.09038i) q^{51} +11.5873i q^{52} -41.5179 q^{53} +(30.2571 - 23.2918i) q^{54} -7.48331i q^{56} +(66.7650 - 14.8377i) q^{57} -22.0417i q^{58} -55.1602i q^{59} -94.7726 q^{61} +36.1853 q^{62} +(-10.0856 - 21.5704i) q^{63} +8.00000 q^{64} +(7.34084 + 33.0316i) q^{66} +77.1064i q^{67} -18.7156 q^{68} +(102.465 - 22.7715i) q^{69} +18.0046i q^{71} +(23.0597 - 10.7820i) q^{72} -33.2022i q^{73} +54.4342i q^{74} +45.5959 q^{76} +21.1014 q^{77} +(5.33255 + 23.9949i) q^{78} +54.9427 q^{79} +(51.9374 - 62.1571i) q^{81} -49.6477i q^{82} -78.6593 q^{83} +(-3.44388 - 15.4964i) q^{84} -83.5731i q^{86} +(-10.1438 - 45.6439i) q^{87} +22.5583i q^{88} +120.028i q^{89} +15.3285 q^{91} +69.9764 q^{92} +(74.9326 - 16.6528i) q^{93} +1.46395 q^{94} +(16.5664 - 3.68167i) q^{96} +24.5127i q^{97} -9.89949 q^{98} +(30.4028 + 65.0234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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